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ANTS
2006
Springer
95views Algorithms» more  ANTS 2006»
14 years 2 months ago
Constructing Pairing-Friendly Elliptic Curves with Embedding Degree 10
We present a general framework for constructing families of elliptic curves of prime order with prescribed embedding degree. We demonstrate this method by constructing curves with ...
David Freeman
JOC
2010
106views more  JOC 2010»
13 years 9 months ago
A Taxonomy of Pairing-Friendly Elliptic Curves
Elliptic curves with small embedding degree and large prime-order subgroup are key ingredients for implementing pairingbased cryptographic systems. Such “pairing-friendly” curv...
David Freeman, Michael Scott, Edlyn Teske
PAIRING
2007
Springer
108views Cryptology» more  PAIRING 2007»
14 years 4 months ago
Constructing Pairing-Friendly Genus 2 Curves with Ordinary Jacobians
We provide the first explicit construction of genus 2 curves over finite fields whose Jacobians are ordinary, have large prime-order subgroups, and have small embedding degree. ...
David Freeman
SACRYPT
2005
Springer
112views Cryptology» more  SACRYPT 2005»
14 years 4 months ago
Pairing-Friendly Elliptic Curves of Prime Order
Previously known techniques to construct pairing-friendly curves of prime or near-prime order are restricted to embedding degree k 6. More general methods produce curves over Fp wh...
Paulo S. L. M. Barreto, Michael Naehrig
PAIRING
2009
Springer
124views Cryptology» more  PAIRING 2009»
14 years 5 months ago
Fast Hashing to G2 on Pairing-Friendly Curves
When using pairing-friendly ordinary elliptic curves over prime fields to implement identity-based protocols, there is often a need to hash identities to points on one or both of ...
Michael Scott, Naomi Benger, Manuel Charlemagne, L...